Which function matches this graph?
f(x)=x2−3f ( x ) = x 2 − 3
f(x)=x2+9f x = x 2 + 9
f(x)=x2−6x+9f ( x ) = x 2 − 6 x + 9
f(x)=x2+6x+9f ( x ) = x 2 + 6 x + 9
Answer:
[tex]\large\boxed{\sf f(x) = x^2-6x+9}[/tex]
Step-by-step explanation:
We are here given a graph of a equation and we are interested in finding the equation .
From the given graph we can see that it cuts the x axis at point (3,0) . This graph represents a quadratic function and its two zeroes are 3,3 . We can write the equation using the two zeroes .
Say if the zeroes of the quadratic equation are p and q , then the quadratic equation can be written as ,
[tex]\longrightarrow (x-p)(x-q)=0 [/tex]
And the quadratic function can be written as ,
[tex]\longrightarrow f(x)= k[ (x-p)(x-q)][/tex]
where k is a constant .In this case k = 1 . So we can write the function as ,
[tex]\longrightarrow f(x) = (x-3)(x-3)[/tex]
Distribute ,
[tex]\longrightarrow f(x)= x (x-3)-3(x-3)[/tex]
Simplify by opening the brackets,
[tex]\longrightarrow f(x) = x^2-3x -3x +9 [/tex]
Add like terms,
[tex]\longrightarrow \underline{\underline{f(x) = x^2-6x+9}}[/tex]
And we are done!
Which one of the following points lies on the
line y= 2x - 3
Answer:
its c (4,1)
Step-by-step explanation:
The required point for the given line is (0, -3). The correct option is (D).
What is a linear equation?A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.
It can be represented as a straight line on a graph.
The equation of the given line is y = 2x - 3.
In order to find the point lying on it, consider each of the options one by one as follows,
(a) (2 , 3)
Substitute x = 2 and y = 3 in the given equation to obtain LHS and RHS as,
LHS = y
= 7
RHS = 2x - 3
= 2 × 2 - 3
= 1
Since, LHS ≠ RHS, the given point is not the solution.
(b) (-2, -1)
Substitute x = 2 and y = 3 in the given equation to obtain LHS and RHS as,
LHS = y
= 7
RHS = 2x - 3
= 2 × -1 - 3
= -6
Since, LHS ≠ RHS, the given point is not the solution.
(c) (4, 1)
Substitute x = 2 and y = 3 in the given equation to obtain LHS and RHS as,
LHS = y
= 4
RHS = 2x - 3
= 2 × 1 - 3
= -1
Since, LHS ≠ RHS, the given point is not the solution.
(d) (0, -3)
Substitute x = 2 and y = 3 in the given equation to obtain LHS and RHS as,
LHS = y
= -3
RHS = 2x - 3
= 2 × 0 - 3
= -3
Since, LHS = RHS, the given point is the solution.
Hence, the point (0, -3) is the solution of the given equation.
To know more about linear equation click on,
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Enter the value for x that makes the equation 7x+5-x+6=53
Answer:
x = 7
Step-by-step explanation:
7x + 5 - x + 6 = 53 , that is
6x + 11 = 53 ( subtract 11 from both sides )
6x = 42 ( divide both sides by 6 )
x = 7
2 square root of x / square root of x multiplied by 3
Answer:
There are two possible answers to this question. if the demoninator has the three on the outside of the square root your answer is 2/3. If your demoninator has the three inside the square root your answer is [tex]\frac{2\sqrt{3} }{3}[/tex] or 1.15. Let me know if this helps!
Maggie bought 30 pounds of produce to feed her hungry hippopotamus. Bananas cost $1 per pound; guavas cost $2 per pound; and dragon fruit costs $3 per pound. Maggie spent $46. The weight of the bananas that Maggie bought was twice the weight of the guavas and dragon fruit combined. Which system of equations in three variables can be used to determine how many pounds of each fruit Maggie bought?
Answer: Required system:
x+y+z=30
x+2y+3z = 46
x= 2y+2z
Step-by-step explanation:
let x= Number of pounds of bananas
y = Number of pounds of guavas
z = Number of pounds of dragon fruit
According to the question,
x+y+z=30 (i) (total fruits bought = 30 pounds)
Bananas cost $1 per pound; guavas cost $2 per pound; and dragon fruit costs $3 per pound and total cost = $46.
∴ x+2y+3z = 46 (ii)
Also, weight of the bananas= 2 (weight of the guavas+ weight of dragon fruit)
∴ x = 2(y+z)
⇒x= 2y+2z (iii)
from (i), (ii) and (iii)
x+y+z=30
x+2y+3z = 46
x= 2y+2z
are the equations for the required system.
Work out 4/5 - 3/20 - 2/10
Answer:
9/20
Step-by-step explanation:
LCM of 5, 20, and 10 = 20
4/5
= 4/5 x 4/4
= ( 4 x 4 )/( 5 x 4 )
= 16/20
2/10
= ( 2/10 ) x ( 2/2 )
= ( 2 x 2 )/( 10 x 2 )
= 4/20
4/5 - 3/20 - 2/10
= 16/20 - 3/20 - 4/20
= ( 16 - 3 - 4 )/20
= ( 16 - 7 )/20
= 9/20
Answer:
9/20
Step-by-step explanation:
First, you need to find common denominators between all of the fractions.
All of these denominators can be multiplied by a whole number to equal 20.
For 4/5, multiply both the numerator and the denominator by 4 to get 16/20
Leave 3/20 alone
For 2/10, multiply both the numerator and the denominator by 2 to get 4/20
Now you have 16/20 - 3/20 - 4/20
= 9/20
A cheetah runs at a speed of 54 miles for every hour. If the distance traveled, I miles, is d and time, in hours, is t, which equation shows the e eels between d and t?
Answer:
I believe you already selected the correct answer in the picture
Need help mark you as brailiest
Answer:
C,F
Step-by-step explanation:
Quadrilateral DEFG has coordinates D (2, 1), E (2, 6), F (5, 6), and G (5, 1). How can quadrilateral DEFG be classified?
Group of answer choices
rhombus but not a square
parallelogram but neither a rhombus nor a rectangle
rectangle but not a square
square
Answer:
Rectangle but not a square
Step-by-step explanation:
Let's start by determining if it's a parallelogram.
The slope of side DE is undefined.
The slope of side EF is 0.
The slope of side FG is undefined.
The slope of side DG is 0.
Thia means we have 2 pairs of opposite parallel sides, meaning DEFG is a rhombus.
Now, let's determine if it's a rectangle. Since the slope of
side DE is undefined and the slope of side EF is 0, sides DE and EF are perpendicular. This means that angle DEF is a right angle, and thus DEFG is a rectangle.
To determine if DEFG is a rhombus, we can find the lengths of adjacent sides DE and EF.
The length of DE is 5.
The length of EF is 3.
Since the pair of consecutive sides (sides DE and EF) aren't congruent, DEFG is not a rhombus.
Since DEFG is not a rhombus, it also cannot be a square.
This means DEFG is a rectangle, but not a square.
i don’t really understand this
Answer:
you put the -3 where the x's are
Step-by-step explanation:
f(x)= -2(-3)^2 - 3(-3) + 6
i think i hope thats right
Answer:
Plug in -3 into all the x's are
Step-by-step explanation:
f(x)= -2(-3)²-3(-3)+6
There are 35 ducks and pigs total on the farm. in total the number amount of legs they have among them is 98. assuming each duck has 2 legs and each pig has 4, how many ducks and how many pigs are in the field
Answer:
I believe there are 21 ducks and 14 pigs in the field
Step-by-step explanation
x+y=35
2x+4y=98
2x+2y=70
2x+4y=98
-2y=-28
y=14
x+14=35
x=35-14
x=21
21=ducks
14=pigs
What is the remainder when you divide: ( 4x^2 − 11x + 8 ) ÷ ( x + 2 )?
g = 1, h = 2
7 + g − 8 + 2h + 4g
Answer:
7+1-8+2(2)+4(1)
= -1+4+4
=7
Answer:
8
Step-by-step explanation:
Given:
g = 1, h = 2
7 + g − 8 + 2h + 4g
Solve:
Since g = 1 and h =2
Substitute
7+(1)-8+2(2)+4(1)
= 7+(1)-8+4+4(1)
= 7 + (1)-8+4+4
= 8 -8 + 4 + 4
= 4 + 4
=8
Hence, Answer = 8
~lenvy~
Can someone help with all these problems?. Give me the right solutions and the winner will recive a brainly.
Answer: For the first one wouldnt it be like:
ht=10(r)+5
Step-by-step explanation:
Suppose the length of the diagonal of this rectangular television screen is 29 inches and the length of the base of the screen is 21 inches.
What is h, the height of the television screen?
A. 25 in.
B. 21 in.
C. 15 in.
D. 20 in.
Answer:
D. 20 in
Step-by-step explanation:
3×7=21 is direct or indirect proportion. give a reason for your answer
Arianna and Blair are working on a problem together: Solve x/3 + 8 = -2. Blair thinks the first step is to multiply by 3. Arianna explains that this, not the most efficient way to solve. Explain who is correct and justify your reasoning.
x/3 + 8 = -2
Because x is in a fraction, the most efficient way to solve is to remove the 8 first.
The first step should be to subtract 8 from both sides:
x/3 = -10
Then you would multiply both sides by 3:
x = -30
Blair was correct but Arianna is correct too.
Let's see why :
_________________________________ We're gonna solve it from Blair's method .
[tex] \frac{x}{3} + 8 = - 2 \\ [/tex]
Multiply sides by 3
[tex]x + 24 = - 6[/tex]
Subtract sides minus 24
[tex]x = - 6 - 24[/tex]
[tex]x = - 30[/tex]
_________________________________
The faster way is :
[tex] \frac{x}{3} + 8 = - 2 \\ [/tex]
Subtract sides minus 8
[tex] \frac{x}{3} = - 2 - 8 \\ [/tex]
[tex] \frac{x}{3} = - 10 \\ [/tex]
Multiply sides by 3
[tex]x = - 30[/tex]
It is very easier to calculate -2-8 than -24-6 and also it is very easier to multiply -10 by 3 than multiply 8 by 3 and multiply -2 by 3 and then calculate.
So Arianna is correct.
I think this is the correct answer.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
Sam is a forklift operator at a Los Angeles warehouse. A 500 kg crate arrived from Taiwan. His forklift can load 2,500 lb. He wants to know if it is safe to lift the crate. How many pounds does the crate weigh?
PLZZZ HELP
1 kg = 2.2 pounds ( rounded to the nearest tenth)
500 kg x 2.2 = 1,100 pounds
1100 pounds is less than 2,500 so the forklift can lift it.
Answer:
2,500= 1133.981
Step-by-step
The answer is 1133.981 bc you would have to use the conversion rate of lb to kg, so just 2500 lb × 0.45359237
= 1133.980925 kg
0.45359237 this is the conversion rate therefore 1134 is the answer (was rounded)
This figure represents a piece of a structure that will be built out of sheet metal. The construction crew needs 3 of these pieces.
How much sheet metal is needed to build all 3 pieces.
Enter your answer in the box.
Answer:
702 ft²
Step-by-step explanation:
The total surface area of the prism is the sum of the areas of its 7 faces.
lateral area
The width of each rectangular face is 8 ft. The total length of all of the rectangular faces is equal to the perimeter of the base:
7 ft +5 ft +3 ft +5 ft + 2 ft = 22 ft
So, the rectangular area is ...
A = LW = (8 ft)(22 ft) = 176 ft²
__
base area
The area of each base is equivalent to the area of a 5 ft×7 ft rectangle with a 3 ft×4 ft right triangle cut off one corner. The base area will be ...
A = LW -1/2bh
A = (5 ft)(7 ft) - 1/2(3 ft)(4 ft) = 29 ft²
__
area of one
So the total surface area of one structure is ...
lateral area + 2×(area of one base)
= 176 ft² +2(29 ft²) = 234 ft²
__
If 3 pieces are needed, the total amount of sheet metal needed for their construction is ...
(234 ft²) × 3 = 702 ft² . . . . needed to build all 3 pieces
Answer:
the answer is 702 I took the test
There is a bag filled with 4 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?
Answer:
The probability of getting exactly iblue is [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
[tex]from\ the\ given\ condition.[/tex]
[tex]We\ only\ have\ two\ way.[/tex]
[tex]One\ way\ is\ the\ first\ one\ take\ the\ blue.[/tex]
[tex]one\ but\ the\ second\ one\ take\ red.\ one.[/tex]
[tex]Another\ way\ is\ the\ first\ one\ take\ the\ red.[/tex]
[tex]one\ but\ the\ second\ one\ take\ the\ blue.[/tex]
[tex]one.[/tex]
[tex]so.\ P_1=\frac{4}{9}\times\frac{5}{8}=\frac{5}{18}[/tex]
[tex]P_2=\frac{5}{9}\times\frac{4}{8}=\frac{5}{18}[/tex]
[tex]so.\ we\ have\ p=p_1+p_2=\frac{5}{18}+\frac{5}{16}=\frac{5}{9}[/tex]
I hope this helps you
:)
The width of a rectangular flower shop is 20 feet less than twice the length. The perimeter is more than 70 feet. Which inequality can be used to find a possible length x of the shop in feet?
A. x+ (2x - 20) > 70
B. 2x + 2(2x - 20) > 70
C. x + (x - 20) > 70
D 2x + 2(x - 20) >70
Answer:
what is it
Step-by-step explanation:
The perimeter is represented by the inequality 2x + 2(2x - 20) > 70. Then the correct option is B.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length. The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
The width of a rectangular flower shop is 20 feet less than twice the length.
W = 2L - 20
The perimeter is more than 70 feet. Then the inequality is given as,
P < 2(L + W)
70 < 2(L + 2L - 20)
70 < 2L + 2(2L - 20)
Replace L with x, then we have
2x + 2(2x - 20) > 70
The perimeter is represented by the inequality 2x + 2(2x - 20) > 70. Then the correct option is B.
More about the perimeter of the rectangle link is given below.
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Can someone please help me with this by doing L hospitals rule?
Answer: [tex]\frac{-m^2+n^2}{2}[/tex]
If the font is too small, it says (-m^2+n^2)/2
==============================================
Explanation:
If you plug x = 0 into the original expression, then you'll get the indeterminant form 0/0 after simplifying.
Recall that cos(0) = 1
So we use L'Hospitals rule to derive the numerator and denominator separately (don't use the quotient rule)
[tex]\displaystyle \lim_{x\to0} \frac{\cos(mx)-\cos(nx)}{x^2}\\\\\\\displaystyle \lim_{x\to0} \frac{-m\sin(mx)+n\sin(nx)}{2x}\\\\\\[/tex]
Plug x = 0 into this new expression. You should get 0/0 again here as well, which means you'll have to do another round of L'Hospital
[tex]\displaystyle \lim_{x\to0} \frac{-m^2\cos(mx)+n^2\cos(nx)}{2}\\\\\\[/tex]
Now plugging in x = 0 leads to something that isn't indeterminant
Evaluating the limit gets us
[tex]\displaystyle \lim_{x\to0} \frac{-m^2\cos(mx)+n^2\cos(nx)}{2}\\\\\\=\frac{-m^2\cos(m*0)+n^2\cos(n*0)}{2}\\\\\\= \frac{-m^2+n^2}{2}\\\\\\[/tex]
Find the value of x.
x = 4
Step-by-step explanation:
21x + 6 = 90°
21x = 90 - 6
21x = 84
x = 84/21
x = 4
If the equation 2x
2 – 8x – 42 = 0 is solved by factoring, what is its positive
solution set?
A. {-3} B. {5} C. {6} D. {7}
Answer:
B.{5}
Step-by-step explanation:
2-8x-42=0
(÷2), we get,
1-4x-21=0
-4x-20=0
-4x=20
x=20÷(-4)
x=(-5)
since the question asks for a positive set, the answer is [x=5]
The positive solution set is D. {7}.
What is a set ?A set is a well defined collection of objects written by commas and closed by second brackets.
According to the given question the equation 2x² - 8x - 42 = 0 have two factors and we have write the positive factor in form of a set.
2x² - 8x - 42 = 0
x² - 4x - 21 = 0
x² -7x + 3x - 21 = 0
x(x-7) + 3(x - 7) = 0
(X+3) = 0 OR (x-7) = 0
x = -3 OR x = 7.
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factorize the following expression completely 2x*2 - x - 6
Answer:
3(x-2)
Step-by-step explanation:
Factor 2x(2)−x−6
=> 3x−6
=>3(x−2)
Answer:
=> 3(x−2)
Solve and graph the solution to the inequality. -4z+8<-27+z
Answer:
z>7
Step-by-step explanation:
subtract z from both sides, then subtract 8 from both sides. The, divide both by the -5 (and remember to flip the sign since you divided by a negative number).
Lines AB and CD and are parallel. Find the measures of the three angles in triangle ABF.
Answer: ∠B = 42° ∠A = 23° ∠F = 115°
Step-by-step explanation:
∠B≅∠C alternate interior angles 42°
∠CDF is supplementary to ∠CDE,
so m∠CDF = 23° and ∠FAB≅∠CDF so m∠FAB= 23°
also ∠A ≅ CDE corresponding angles 157° ∠FAB is suplementary to ∠A
so 180 - 157 = 23 gives the m∠FAB
The sum of the angles of a triangle is 180°, so m∠AFB = 180 -(23 +42)
180- 65 = 115 = m∠F
If VZ=p–7 and WY=p–21, what is the value of p?
Answer:
35
Step-by-step explanation:
By the triangle midsegment theorem, 2(WY)=VZ.
So, 2(p-21)=p-7, meaning p=35.
Which equation represents the data in the table?
Answer:
C
Step-by-step explanation:
I usually solve these problems by process of elimination, but you can solve these differently!
A. y=1/2x. This would basically mean to divide x by 2 to get y. We can see 2/2=1, 4/2=2, 6/2=3, and 8/2=4. This does not match up with the table, where the numbers are 1, 5, 9, and 13. 1, 5, 9, and 13 are not equal to 1, 2, 3, and 4. So A is not our answer.
B. y=x-1. This would mean to subtract 1 from x to get y. 2-1=1, 4-1=3, 6-1=5, and 8-1=7. This does not match up with the table. 1, 3, 5, and 7 is not equal to 1, 5, 9, and 13.
C. y=2x-3. This would mean we would multiply 2 by x and subtract 3 to get y. 2*2-3=1, 2*4-3=5, 2*6-3=9, and 2*8-3=13. 1, 5, 9, and 13 are equal to 1, 5, 9, and 13, so this will be our answer.
D. y=3x-5. This would mean we would multiply 3 by x and subtract by 5. 3*2-5=1, 3*4-5=7, 3*6-5=13, and 3*8-5=21. This is not equal to 1, 5, 9, and 13.
What is the answer? (-3,7x) x (5.1y)
(−3.7x)(5.1y)
= −18.87xy